Do you mean shudder? (not shutter)

If your idle roughness is rhythmic, then you have a weak or missing cylinder and that would be your unsmooth takeoff.

Are you absolutely certain that the front and centre U-joints are lined up exactly? The yoke at each end of the front driveshaft tube (the one with the slip joint in it) must be on the SAME plane. There are 18 splines leaving two acceptable positions and 16 that are wrong. A one tooth mismatch will cause a vibration under load.

A transmission shudder, called clutch chatter, would be load related and is usually a violent shaking and indicates the end of life for at least one involved clutch pack. Other than the common rear bushing wear, it is very unlikely that the tranmission is your source. More directly; look outside the transmission, not in it.